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-Factorial ANOVA in SPSS
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-Factorial ANOVA in SPSS
Statistics for the Social Sciences
Psychology 340 Spring 2006
Factorial ANOVA
Outline
Statistics for the Social Sciences
? Basics of factorial ANOVA
—Interpretations
Main effects
Interactions
—Computations
—Assumptions, effect sizes, and power
— Other Factorial Designs
More than two factors
Within factorial ANOVAs
Outline
Statistics for the Social Sciences
? Basics of factorial ANOVA
-Interpretations
Main effects
Interactions
—Computations
—Assumptions, effect sizes, and power
— Other Factorial Designs
Within factorial ANOVAs
Mixed factorial ANOVAs
Assumptions in Two-Way ANOVA
Statistics for the
Social Sciences ? ”
Populations follow a normal curve
Populations have equal variances
Assumptions apply to the populations that go with each cell
Effect Size in Factorial ANOVA
Statistics for the Social Sciences(completely between groups)
Statistics for the Social Sciences
SSa SSa
■ SSt 两-SSa - SS^ ■ SSa + ss品
SSb
SSt 两—SSb - ss^
SSb
SSb + SS切
SSab
SSt两
SSa
Statistics for the Social SciencesTABLE 10.16
Statistics for the Social Sciences
TABLE 10.16
Approximate Sample Size Needed in Each Cell for 80% Power (.05 significance level)
Approximate Number of Participants Needed in Each Cell {Assuming Equal Sample Sizes) for 80% Power for Studies Using a2x2or2x3 Analysis of Variance, Testing Hypotheses at the .05 Significance Level
Effect Size
Sm^l (Ff = .01)
Medium (梓=.06)
Large
(R2 = . 14)
2 X 2: All effects
197
33
14
2 X 3: Two-level main effect
132
22
9
Three-level mairi effect and interaction
162
27
11
Statistics for the Social Sciences
Other ANOVA designs
Basics of repeated measures factorial ANOVA
-Using SPSS
Basics of mixed factorial ANOVA
-Using SPSS
? Similar to the between groups factorial ANOVA
— Main effects and interactions
—Multiple sources for the error terms (different denominators for each main effect)
Example
Statistics for the
Social Sciences ? ”
? Suppose that you are interested in how sleep deprivation impacts performance? You test 5 people on two tasks (motor and math) over the course of time without sleep (24 hrs, 36 hrs, and 48 his). Dependent variable is number of errors in the tasks.
-Both factors are manipulated as within subject variables
-Need to conduct a within groups factorial ANOVA
Example
Statistics for the
Social Sciences ? ”
Factor B: Hours awake
24 36 48
E] B3
A】
Motor
Factor A:
Task
a2
Math
0
0
6
1
3
5
0
1
5
4
5
9
0
1
5
1
1
4
1
2
6
0
1
6
3
2
4
1
3
4
ExampleStatistics for the
Example
Statistics for the
Social Sciences ? ；
Within factorial ANOVA in SPSS
Statistics for the Social Sciences
Each condition goes in a separate column
-It is to your benefit to systematically order those columns to reflect the factor structure
Make your column labels informative
Analyze ?> General Linear Model ?> Repeated measures
Enter your factor 1 & number of levels, then factor 2 & levels, etc. (remember the order of the columns)
Tell SPSS which columns correspond to which condition
As was the case before, lots of output
Focus on the within-subject effects
Note: each F has a different error term
Source
ss
A
1.20
Error (A)
13.13
B
104.60
Error (B)
6.10
AB
2.60
Error (AB)
8.10
df
MS
F
P
1
1.20
0.37
0.58
4
3.28
2
52.30
69.00
<0.01
8
0.76
2
1.30
1.29
0.33
8
1.01
Example
Example
Example
Example
Statistics for the
Social Sciences ‘
? It has been suggested that pupil size increases during emotional arousal. A researcher presents people with different types of stimuli (designed to elicit different emotions). The researcher examines whether similar effects are demonstrated by men and women.
Type of stimuli was manipulated within subjects
Sex is a between subjects variable
Need to conduct a mixed factorial ANOVA
ExampleStatistics for the
Example
Statistics for the
Social Sciences ? ；
ExampleStatistics for the
Example
Statistics for the
Social Sciences ? ”
Factor B: Stimulus
Neutral Pleasant Aversive
E] B3
4
8
3
3
6
3
A.
2
5
2
Men
3
3
6
FactorA:
3
8
1
Sex
3
6
2
2
4
1
a2
4
6
6
Women
1
7
3
3
5
2
Mixed factorial ANOVA in SPSS
Statistics for the Social Sciences
Each within condition goes in a separate column
-It is to your benefit to systematically order those columns to reflect the factor structure
Make your column labels informative
Each between groups factor has a column that specifies group membership
Analyze ?> General Linear Model ?> Repeated measures
Enter your within groups factors: factor 1 & number of levels, then factor 2 & levels, etc. (remember the order of the columns)
Tell SPSS which columns correspond to which condition
Enter your between groups column that specifies group membership
As was the case before, lots of output
Need to look at the within-subject effects and the between groups effects
Source
ss
Between
Sex (A)
0.83
Error (A)
20.00
Within
Stimulus (B)
58.10
Sex * Stimulus
0.07
Error (B)
39.20
df
MS
F
p
1
0.83
0.33
0.58
8
2.50
2
29.00
11.85
0.001
2
0.03
0.01
0.97
16
2.45
Factorial ANOVA in Research Articles
Statistics for the Social Sciences
A two-factor ANOVA yielded a significant main effect of voice, F(2? 245) = 26.30,p < .001. As expected, participants responded less favorably in the low voice condition (M= 2.93) than in the high voice condition (M= 3.58). The mean rating in the control condition (M= 3.34) fell between these two extremes? Of greater importance, the interaction between culture and voice was also significant, F(2, 245) = 4.1 <.02.
Recruiting
Statistics for the
Social Sciences ‘
Looking for a teaching experience?
Enjoy (tolerate?) statistics
I am looking for Undergraduate Teaching Assistant(s) for PSY 138 next semester
If interested:
1. E-mail me about your interest: jccutti@ilstu.edu